What is the Greatest Common Factor of 12309 and 12321?

Greatest common factor (GCF) of 12309 and 12321 is 3.

GCF(12309,12321) = 3

We will now calculate the prime factors of 12309 and 12321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12309 and 12321.

How to find the GCF of 12309 and 12321?

We will first find the prime factorization of 12309 and 12321. After we will calculate the factors of 12309 and 12321 and find the biggest common factor number .

Step-1: Prime Factorization of 12309

Prime factors of 12309 are 3, 11, 373. Prime factorization of 12309 in exponential form is:

12309 = 3¹ × 11¹ × 373¹

Step-2: Prime Factorization of 12321

Prime factors of 12321 are 3, 37. Prime factorization of 12321 in exponential form is:

12321 = 3² × 37²

Step-3: Factors of 12309

List of positive integer factors of 12309 that divides 12309 without a remainder.

1, 3, 11, 33, 373, 1119, 4103

Step-4: Factors of 12321

List of positive integer factors of 12321 that divides 12309 without a remainder.

1, 3, 9, 37, 111, 333, 1369, 4107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12309 and 12321. The biggest common factor number is the GCF number.
So the greatest common factor 12309 and 12321 is 3.

Also check out the Least Common Multiple of 12309 and 12321